On the sister site, someone had this signature as below and a thread was raised to discuss it....

Nibbana does not exist when there's no arahant or buddha in the world to experience it
IF (A) Nibbana does not exist when there's no arahant or buddha in the world to experience it
THEN (B) Nibbana is subjective, a psychological phenomenon

IF (B) Nibbana is subjective, a psychological phenomenon
THEN (C) Nibbana is a mental fabrication, which being dependent on another cannot be permanent

IF (C) Nibbana cannot be permanent
THEN (D) There's no true liberation from suffering

So, does nibbana exist when there's no arahant or buddha in the world or not?
Where's the flaw in the argument?

Technically nirvana isn't experienced in the first place, so the logic which ensues based on that initial premise is flawed to begin with...

Malcolm wrote:Aryadeva clearly states in 400 Verses:

[Since] there are no aggregates in nirvana,
a person cannot possibly be [in nirvana].

Candrakirti comments on this:

If there are aggregates in nirvana, there is also a person. At that time, because they exist [i.e. aggregates and persons], in contradiction with sūtra there will be a support that turns into nirvana, and samsara cannot be transcended.

Nāgārjuna's examination of the Tathāgata and Nirvana in his MMK further demonstrate how the initial premise is flawed.

Look carefully at the derivation of the word 'exist'. It comprises two particles: 'ex-', seen in 'external', 'exile', etc, denoting 'apart from' or 'outside of'.

-'ist' denotes 'is' or simply 'to be'.

So 'ex-ist' means 'to be apart' - to be an identifiable and separate from other things. Existence is the state of being something, being this as distinct from that.

So manifest objects exist: chairs and tables, mountains and rivers, stars and planets. These are all existing things in the domain of the natural sciences, which is the 'phenomenal realm' or the 'manifest realm'. I think when it is said 'whatever exists is impermanent', it is in reference to these types of things - 'compounded', 'fabricated', 'made' and so on.

So nirvana is not something that exists, when 'existence' is understood in those terms. It is certainly not amongst any of the objects of perception or the realm of existing things. In that sense it doesn't exist.

Now consider the meaning of another word, 'ecstacy'. That is actually derived from a similar root, 'ecs' being the same particle as above; and '-stasis', denoting 'stable, inert, unchanging'. So the 'ecstatic' state is 'outside'or 'apart from' the normal 'stasis', which represents the conditioned state of mind. I think this is why it is said that 'no person exists in nirvana' - because the mental structure (vikalpa) which construct the sense of persons and objects of perception, is dissolved in that state. Hence the practice of dhyana which is associated with reaching states such as 'the formless realm'.

The point is always to 'practice~realize' such states, not to say what they are or name them, because in doing that, they are implicitly being made part of the manifest realm - which of course they are actually not.

Abhidamma texts speak of nirvana as an ultimate in that it can't be stripped down to something more essential or basic. In these texts it is referred to as the unconditioned or deathlessness or baselessness. Actually even in Dzogchen texts the so-called ultimate nature of reality is said to be baseless. But does this mean that it has no existence? Actually no. Baselessness does exist. It is a very natural part of experience. It's apart of how reality is.

Nirvana is pointing to what is fundamental, invariant and pervasive. It is not a creation and so it is not a thing. But it does have consequences. It's connected with energy. It's a pervasive baselessness that has power due to it being unconditioned, baseless, unborn.

The Blessed One said:

"What is the All? Simply the eye & forms, ear & sounds, nose & aromas, tongue & flavors, body & tactile sensations, intellect & ideas. This, monks, is called the All. Anyone who would say, 'Repudiating this All, I will describe another,' if questioned on what exactly might be the grounds for his statement, would be unable to explain, and furthermore, would be put to grief. Why? Because it lies beyond range." Sabba Sutta.

Baselessness or unconditioned isn't a thing - so it isn't a conditioned state or object. But it does have energy and consequences. This is a key issue that sometimes gets ignored. It is not that you can find this baselessness and yet this not finding has consequences and therefore it is wrong to say that baselessness is simply a nothing or not there. The 'not' or negative is that it can't be found or seen and so it is not an object that is eternal. And yet this not finding and not seeing has positive consequences - an energy that is entirely natural and with us right now.

The Blessed One said:

"What is the All? Simply the eye & forms, ear & sounds, nose & aromas, tongue & flavors, body & tactile sensations, intellect & ideas. This, monks, is called the All. Anyone who would say, 'Repudiating this All, I will describe another,' if questioned on what exactly might be the grounds for his statement, would be unable to explain, and furthermore, would be put to grief. Why? Because it lies beyond range." Sabba Sutta.

'Sensory appearances, moreover, arise naturally due to the dynamic energy [rtsal] of awareness [rig pa], and so their nature is described in a purely symbolic way as one of interdependent connection [dependent origination]. Even in the very moment that things seem to arise due to that dynamic energy they do not do so without being subject to extremes or divisions - with no question of whether or not something arises - and even 'dynamic energy' is just a symbolic term, with no finite essence whatsoever. So within the context [dharmatā] that is never subject to transition or change, nothing strays in the slightest from awakened mind.'

Even the statement that things arise as samsara and nirvana due to the dynamic energy [rtsal] of awareness [rig pa] is merely conventional, for in essence nothing has ever existed as anything in the slightest - nothing being distinct in itself as the process of samsara or nirvana arising, or as some 'thing' that arises."
- chos dbyings rin po che'i mdzod ces bya ba'i 'grel pa

"I manifest in everything in the universe. Although I appear everywhere, I cannot be seen. Relax in the realm which cannot be seen. I pervade the entire animate and inanimate universe. Although I pervade everything, I cannot be identified. Relax in the realm beyond identification. I am the foundation of everything. Because I have no concrete base, I cannot be accomplished. Relax in the realm beyond accomplishment. I distinguish everything. Although I am the expert distinguisher, I do not even have one concept. Relax in the realm beyond distinctions. I manifest in everything, but I cannot be manifested by anything. Relax in the realm beyond manifestation."

The Blessed One said:

"What is the All? Simply the eye & forms, ear & sounds, nose & aromas, tongue & flavors, body & tactile sensations, intellect & ideas. This, monks, is called the All. Anyone who would say, 'Repudiating this All, I will describe another,' if questioned on what exactly might be the grounds for his statement, would be unable to explain, and furthermore, would be put to grief. Why? Because it lies beyond range." Sabba Sutta.

This is from a commentary on the Kunjed Gyalpo. So this is coming from a Dzogchen POV.

The Blessed One said:

"What is the All? Simply the eye & forms, ear & sounds, nose & aromas, tongue & flavors, body & tactile sensations, intellect & ideas. This, monks, is called the All. Anyone who would say, 'Repudiating this All, I will describe another,' if questioned on what exactly might be the grounds for his statement, would be unable to explain, and furthermore, would be put to grief. Why? Because it lies beyond range." Sabba Sutta.

In an ultimate sense, nibbāna does not exist at all. What exists is defined as that which can be known by the mind. Anything that cannot be known by the mind does not exist. And conventionally, things can exist as in fallacy or in reality. But in the ultimate reality, things do not exist in the ways that concepts and language imply they do. Things would only exist as in deepest facts i.e. it is beyond mind and beyond concepts and words in the sense that it is beyond our usual ways of perceiving things.

Nibbāna can be known as the ultimate cessation of events - a non-dependent nature. Whereas, samsāra literally means ‘continuous flow’- referring to a repeating cycle of birth, life, death and re-birth. In other words, there would be plentiful of events within samsāra - a dependent nature, but why is it so? It is because of the mind arising. As the Buddha has mentioned, mind is the forerunner of all states. This means the truth orientation within samsāra is dependent on the observer (i.e. the subject’s mind) to provide with the description, definition, recognition, valuation, etc. on the other side of the object or matter. And the truth conclusion varies among different observers or minds.

The conclusion is that nibbāna exists under the conventional perspective and does not exist under the ultimate perspective.

The principle-in-effect: -
No mind, no dependent nature, no existence - the eternal bliss of nibbāna.

In my opinion a lot about Nirvana is basically what makes Buddhism mostly a religion(defined as a system of belief which depends on premises that cannot be easily and independently verified by individuals who do not subscribe to the system of belief).

Because Nirvana is beyond concepts that means it can't be described, only experienced. The problem is that in order to experience it you have to put yourself at risk to not be able to evaluate it objectively. You can hear about Nirvana from other people but they run the same risk that you do in that they had to work very hard to get a glimpse at Nirvana.

Therefore for most people in order to be practicing Buddhist you have to take the following things on faith.

1. Nirvana exists.
2. The state of Nirvana is, from the point of view that such things can be evaluated, a superior state of existence than the one that we currently exist in.

One might say that these two points of faith are less important for Mahayana Buddhists than Thervadin Buddhists because Mahayana Buddhists strive to achieve a state between Nirvana and Samsara. I would disagree with this and say that the first two points are actually even more important for the Mahayana.

Consider for a second. The stated goal of Mahayana Buddhism is to bring everyone to Nirvana. In order for this to be an ethical goal the Mahayana Buddhist has to believe that not only is Nirvana achievable and "good" but that it is "good" for all sentient beings everywhere. You have to believe that unlike, say, Italian food, everyone will consider Nirvana infinitely better than the existence we currently have.

IN THIS BOOK IT IS SPOKEN OF THE SEPHIROTH & THE PATHS, OF SPIRITS & CONJURATIONS, OF GODS, SPHERES, PLANES & MANY OTHER THINGS WHICH MAY OR MAY NOT EXIST. IT IS IMMATERIAL WHETHER THEY EXIST OR NOT. BY DOING CERTAIN THINGS CERTAIN RESULTS FOLLOW; STUDENTS ARE MOST EARNESTLY WARNED AGAINST ATTRIBUTING OBJECTIVE REALITY OR PHILOSOPHICAL VALIDITY TO ANY OF THEM.

Here the Mahayana view:"Thus, bodhisattvas do not reach or attain nirvana but overcome all delusions, including those that concern the ultimate. goal of nirvana, namely, views that see nirvana as either permanent or not permanent, pleasurable or not pleasurable, self-existent or not selfexistent, pure or not pure. Nirvana is simply the final delusion.[...]
"Another common derivation was to understand nirvana as a combination of the negative prefix nir and the root vri, «to
cover," «to restrain," or "to obstruct." This is most likely the sense understood here, with nir-vana referring to «no walls of the mind," as the word for «walls," avarana, is also derived from vri. Thus, not only do bodhisattvas see through delusions of existence and non-existence, they see through delusions of having stepped past all such delusions.[...]
Ching-mai says, "This explains the liberation door of no desire. Once one realizes dharmas have no nature, and they aren't blocked outside and have no fears inside, they come to know that dharmas are simply delusions, like dreams, and are false and not real. Thus, they see through them and don't give rise to desires." The Heart Sutra - Red Pine

Here the Madhyamaka view: "The nineteenth verse describes how samsara and nirvana are actually undifferentiable:Samsara is not the slightest bit different from nirvana.
Nirvana is not the slightest bit different from samsara.
From the perspective of precise knowledge analyzing the nature of genuine reality, once the true existence of nirvana is refuted, then one realizes that there is no samsara that is even the slightest bit different from nirvana, and no nirvana that is even the slightest bit different from samsara. In short, samsara and nirvana are of the nature of equality, because both have a nature beyond all conceptual fabrications about what it might be, and because both in their true nature are originally pure.
As the Fifth Karmapa Deshin Shekpa states: Whatever is the suchness of samsara, that is nirvana." The Sun of Wisdom: Teachings on the Noble Nagarjuna's Fundamental Wisdom of the Middle Way - Khenpo Tsultrim Gyamtso

Here the Dzogchen view, similar to the Yogacara view:"Ho! Everything - appearance and existence, samsara and nirvana, has a single ground, yet two paths and two fruitions, and magically displays as awareness or unawareness.
Through Kuntuzangpo's prayer, may all beings become Buddhas, completely perfected in the abode of the dharmadhatu. The ground of all is uncompounded, and the self-arising great expanse, beyond expression, has neither the name samsara nor nirvana. Realizing just this you are a Buddha; not realizing this you are a being wandering in samsara." The Prayer of Kuntuzangpo

"People these days use whatever little dharma they know to augment afflictive emotion, and then engender tremendous pride and conceit over it. They teach the Dharma without taming their own minds. But as with a river rock , not even a hair’s tip of benefit penetrates the other people. Even worse, incorrigible people [are attracted] to this dharma that increases conflict. When individuals who could be tamed by the Dharma encounter such incorrigible, their desire for the sacred Dharma is lost. It is not the fault of the Dharma; it is the fault of individuals." Machik Labdron prophecy.

Here the Mahayana view:"Thus, bodhisattvas do not reach or attain nirvana but overcome all delusions, including those that concern the ultimate. goal of nirvana, namely, views that see nirvana as either permanent or not permanent, pleasurable or not pleasurable, self-existent or not selfexistent, pure or not pure. Nirvana is simply the final delusion.[...]
"Another common derivation was to understand nirvana as a combination of the negative prefix nir and the root vri, «to
cover," «to restrain," or "to obstruct." This is most likely the sense understood here, with nir-vana referring to «no walls of the mind," as the word for «walls," avarana, is also derived from vri. Thus, not only do bodhisattvas see through delusions of existence and non-existence, they see through delusions of having stepped past all such delusions.[...]
Ching-mai says, "This explains the liberation door of no desire. Once one realizes dharmas have no nature, and they aren't blocked outside and have no fears inside, they come to know that dharmas are simply delusions, like dreams, and are false and not real. Thus, they see through them and don't give rise to desires." The Heart Sutra - Red Pine

Here the Madhyamaka view: "The nineteenth verse describes how samsara and nirvana are actually undifferentiable:Samsara is not the slightest bit different from nirvana.
Nirvana is not the slightest bit different from samsara.
From the perspective of precise knowledge analyzing the nature of genuine reality, once the true existence of nirvana is refuted, then one realizes that there is no samsara that is even the slightest bit different from nirvana, and no nirvana that is even the slightest bit different from samsara. In short, samsara and nirvana are of the nature of equality, because both have a nature beyond all conceptual fabrications about what it might be, and because both in their true nature are originally pure.
As the Fifth Karmapa Deshin Shekpa states: Whatever is the suchness of samsara, that is nirvana." The Sun of Wisdom: Teachings on the Noble Nagarjuna's Fundamental Wisdom of the Middle Way - Khenpo Tsultrim Gyamtso

Here the Dzogchen view, similar to the Yogacara view:"Ho! Everything - appearance and existence, samsara and nirvana, has a single ground, yet two paths and two fruitions, and magically displays as awareness or unawareness.
Through Kuntuzangpo's prayer, may all beings become Buddhas, completely perfected in the abode of the dharmadhatu. The ground of all is uncompounded, and the self-arising great expanse, beyond expression, has neither the name samsara nor nirvana. Realizing just this you are a Buddha; not realizing this you are a being wandering in samsara." The Prayer of Kuntuzangpo

Of course there are certian Yogācāra tenets that Dzogchen implements in its system such as eight consciousness model, but when it comes down to the view in principle one can also say that Dzogpachenpo closely resembles the Madhyamaka view (not in praxis, but in principle).

The two quotes you posted above for Madhyamaka and Dzogchen are not all that different since the "ground" (or rather, 'basis') which is mentioned in the Dzogchen quote is original purity... a principle which is also referenced in the Madhyamaka quote: "...both in their true nature are originally pure."